4400 IGCSE Mathematics. Summer 2007. Paper 3H. Q. Working. Answer. Mark.
Notes. 1. (a). 1.9. 89.68. 2. M1 for 8.3, 68.89, 9.1 or 30.90… 7.5703… A1 Accept ...
Mark Scheme (Results) Summer 2007
IGCSE
IGCSE Mathematics (4400_3H)
Edexcel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH
4400 IGCSE Mathematics Summer 2007 Paper 3H Q
1.
Working
(a)
Answer
Mark
2
68.89 9.1 7.5703…
Notes
M1
for 8.3, 68.89, 9.1 or 30.90…
A1
Accept if first 5 figures correct Also accept 7
(b)
2.
(a)
7.57
(−3)2 − 5 × −3
x( x − 5)
,
6889 910
1
B1
ft from (a) if non-trivial ie (a) must have more than 2 d.p. Total 3 marks
2
M1 A1 B2
for substn or 9 or 15 seen cao B1 for factors which, when expanded and simplified, give two terms, one of which is correct SC B1 for x(5 − x) and for x(x − 5x) Total 4 marks
24 (b)
519 910
2
3.
46×3+47×6+48×3+49×5+50×2+51×1 or 138+282+144+245+100+51 or 960 “960” ÷ 20
3
48
M1
for finding at least 4 products and adding
M1 A1
(dep) for division by 20 cao Total 3 marks
Q
4.
Working
(a)
Answer
Mark
translation 3 squares to the right and 1 square down
2
Notes
B2
B1 for translation Accept translate, translated etc B1 for 3 right and 1 down (accept ‘across’ instead of ‘to the right’) or
⎛ 3⎞ ⎜ −1⎟ ⎝ ⎠
but not (3, −1) (b)
rotation of 90° clockwise about (2, −1)
3
B3
These marks are independent but award no marks if answer is not a single transformation
B1 for rotation Accept rotate, rotated etc B1 for 90° clockwise or −90° or 270° B1 for (2, −1) Total 5 marks
5.
(ai) (ii) (b)
78 56 9 + 4 − n = 8 or 13 − n = 8
2 2
5
B1 B1 M1 A1
cao cao Also award for 2n = 25 or 25 on answer line cao Total 4 marks
Q
6.
Working
(a)
Answer
Mark
12 x − 15 − 8 x − 4
2
M1
for at least 3 terms correct inc signs
2
A1 M1
cao for 3 terms correct or y2 + 11y seen
4 x − 19 (b)
y 2 + 3 y + 8 y + 24
A1
y 2 + 11y + 24 (c)
7.
(a)
5p3 + 4 p
38.5 21 38.5 × 60 or = 0.35 ; 21 0.35 60
Notes
2
B2
3
M1
M1 110 (b)
π × 4.19 2 × 38500 2 120 000
3
A1 M2 A1
cao B1 for either 5p 3 or for + 4 p Total 6 marks 38.5 or 1.83 or better 21 38.5 or or 183.3 or better 0.21 21 or 0.35 or 60 38.5 for ‘1.8333…’ ×60 or '0.35' cao M1 for π × (no with digits 419)2 × no with digits 385 for 2 120 000 or for answer which rounds to 2 120 000 Total 6 marks
for
Q
8.
Working
(a)
Answer
Mark
2
270 × 100 4500
6 (b)
117 ×
100 4 .5
3328 100 or 3328 × 1.04 104
3200
M1 A1
2
M1
3
A1 M2
2600 (c)
Notes
A1
for
270 4770 or 0.06 or or 1.06 4500 4500
cao for
117 or 26 seen 4 .5
cao 3328 100 or 3328 × 1.04 104 3328 M1 for , 104% = 3328 or 32 seen 104 cao Total 7 marks
for
Q
9.
Working
(a)
Answer
Mark
5 x − 2x = 7 + 4
2 11 , 3
(b)
2 3
3 oe 4
7 − 2y or 7 − 2y 4 = 4(2y + 3) 4×
Notes
M1
for correct rearrangement
A1
Also accept 2 or more d.p. rounded or truncated e.g. 3.66, 3.67 for clear intention to multiply both sides by 4 or a multiple of 4 For example, award for 7 − 2y or 7 − 2y 4× 4 = 4 × 2y + 3 or 8y + 3 or 2y + 3 × 4 or 2y + 12
M1
7 − 2y = 8y + 12 or simpler
M1
10 y = −5
A1
−
1 2
oe
for correct expansion of brackets (usually 8y + 12 ) or for correct rearrangement of correct terms e.g. 8y + 2y = 7 − 12 for reduction to correct equation of form ay = b
A1 Total 6 marks
Q
Working
Answer
Mark
Notes
Accept decimals in parts (a) and (b)
10.
(a)
150 ×
3
3 5
90 (bi)
4 5
×
5
3 4 12 20
(ii)
2 5
×
1 4
3 5
+ ×
or
3 5
oe
2 4
8 20
or
2 5
oe
3 5
B1
for
M1
for 150 ×
A1
cao Do not accept
M1
for
4 5
seen 3 5
90 150
3 4
× seen
A1 M1
for
M1
(dep) for adding both above products
A1
for
2 1 × 5 4 3 2 × 5 4
8 20
or
or
2 5
SC M1 for
2 5
×
2 5
or
3 3 × 5 5
SC M1 (dep) for adding both above products
oe Total 8 marks
Q
11.
Working
(a) (b)
Answer
Mark
tangent at any point of a circle and the radius at that point are perpendicular
6.92 − 5.7 2 or 47.61 − 32.49 or 15.12 6 . 9 2 − 5 .7 2 3.88844…
2 × 5.7 + 2×"3.88844 ..."
19.2
Notes
1
B1
for mention of tangent and radius or line from centre
5
M1
for squaring and subtracting
M1
(dep) for square root
A1
for 3.89 or better
M1 A1
for 2 × 5.7 + 2 × “3.888…” only for 19.2 or answer which rounds to 19.2 (19.176888…) Total 6 marks
(a)
12.
10, 26, 41, 50, 56, 60
1
B1
cao + ½ sq ft from sensible table ft if 4 or 5 points correct or if points are plotted consistently within each interval (inc end points) at the correct height may be shown on graph or implied by 43, 44 or 45 stated If M1 scored, ft from cumulative frequency graph If no method shown, ft only from correct curve Total 5 marks
(b)
Points correct Curve or line segments
2
B1 B1
(c)
Use of w = 430 on graph
2
M1
Approx 16
Q
13.
Working
Answer
A1
Mark
lines region
4
Notes
B3 B1
B1 for each correct line (full or broken) Ignore additional lines for correct region shaded in or out or for correct region labelled R Total 4 marks
14.
(a)
r2 =
2
A
π A
A
M1
for r 2 =
A1
Ignore ±
M1 A1
for 13.5 seen for answer which rounds to 2.073
π
or r2 = A ÷ π
π (bi)
13.5
(ii)
14.5
2.07296…
π π
4
M1
or 2.14836…
for
14.5
π
or value which rounds to
2.148 or 2.149 cao 2.1
A1
dep on previous 3 marks in (b) Total 6 marks
Q
15.
Working
(ai)
f =
Answer
Mark
k w
4
f =
(ii)
Notes
M1 A1
300000 w
B2
f
w
k 200 k Also award if answer is f = but w k is evaluated as 300 000 in (a) or (b) B1 for graph with negative gradient (increasing or constant) even if it touches or crosses one or both axes e.g.
May be implied by 1500 =
f
O
(b)
f=
300000 1250
2
240
M1 A1
w
for substitution in f =
k w
ft from k Total 6 marks
Q
16.
Working
Answer
(ai) (ii) (iii) (b)
Mark
3b 3b − a 2 3 2 3
or
a 2 3
or a + 2 3
2 3 1 (3b 3
− a) − b
2 3
2
B2
(3b − a) oe
for
2 3
a or
2 3
PQ or k =
2 3
unless clearly
B1 for correct vector statement with at least 3 terms which includes EF (or FE) in terms of capital letters and/or a, b
or (a)(iii) − b or −b + a + or −b + a +
or 2b −
− a) or 3b −
B1 B1 B1
or for expression in terms of a and/or b (need not be simplified) for EF either correct or ft from (a)
a+b−b
or 2b −
1 (3b 3
3
obtained by non-vector method
PQ
or k =
or
a + b or a +
Notes
2 3 2 3
1 (3b − a) 3 1 (a)(ii) 3
eg PQ = PE + EF + FQ PF = PE + EF
(3b − a) (a)(ii)
oe
a = b + EF + FQ
If an attempt is crossed out and replaced, mark all attempts, including crossed out one, and award best mark. Total 5 marks
Q
Working
17.
Answer
Mark
4
16 ⎛ dy ⎞ = ⎟ 2x − ⎜ ⎝ dx ⎠ x2
(2, 12)
(a)
3
1 2
π × 2.8 2 + × 4π × 2.8 2 73.9
(b)
B1
for 2x
B1
for ±
M1
16 "2 x ± 2 "= 0 x
18.
Notes
125 or 5 seen 25 × 73.89...
A1
cao For answer (2, 12) with no preceding marks scored, award B0 B0 M1 A1 Total 4 marks
M2
M1 for each term Also award for values rounding to 24.6 and to 49.2 or 49.3 for 73.9 or for answer which rounds to 73.9
A1 3
3
M1 M1
1850
16 or + 16x −2 2 x
A1
for 25 × (a) or for π × (2.8 × 5)2 + 2π × (2.8 × 5)2 or for substituting r = 2.8 × 5 in the expression used in (a) for 1850 or for any value in range 1846.3 - 1847.5 ft from 25 × (a) Total 6 marks
Q
19.
Working
Answer
Mark
Notes
M1
for correct substitution
x 2 + 9x 2 − 3x − 3x + 1 = 5 or x 2 + 9x 2 − 6 x + 1 = 5
B1
(indep) for correct expansion of (3x − 1)2 even if unsimplified
10 x 2 − 6 x − 4 = 0 (5x + 2)(2 x − 2) = 0 or (5x + 2)( x − 1) = 0 or (10 x + 4)( x − 1) = 0
B1
for correct simplification
B1
for correct factorisation
6
x 2 + (3x − 1)2 = 5
or
6 ± 196 3 ± 49 or 20 10
or
3 49 ± 10 10
x=−
2 5
or for correct substitution into the quadratic formula and correct evaluation of ‘b2 − 4ac’
or x = 1 2 5
x = − , y = −2
1 5
A1
or for using square completion correctly as far as indicated for both values of x
A1
for complete, correct solutions
x = 1, y = 2 Total 6 marks PAPER TOTAL 100 MARKS
14
